Equatorward alongshore winds over major eastern boundary upwelling systems (EBUSs) drive intense upwelling via Ekman dynamics, surfacing nutrient-rich deep waters and promoting marine primary production and fisheries. It is generally thought, dating back to Bakun’s hypothesis, that greenhouse warming should enhance upwelling in EBUSs by intensifying upwelling-favourable winds; yet this has not been tested. Here, using an ensemble of high-resolution climate simulations with improved EBUS representation, we show that long-term upwelling changes in EBUSs differ substantially, under a high-emission scenario, from those inferred by the wind-based upwelling index. Specifically, weakened or unchanged upwelling can coincide with intensified upwelling-favourable winds. These differences are linked to long-term changes of geostrophic flows that dominate upwelling changes in the Canary and Benguela currents and strongly offset wind-driven changes in the California and Humboldt currents. Our results highlight the controlling role of geostrophic flows in upwelling trends in EBUSs under greenhouse warming, which Bakun’s hypothesis overlooked.